###### "Probing the 2D Fermi-Hubbard Model Under a Quantum Gas Microscope"

Ultracold fermionic atoms in optical lattices offer a pristine platform for quantum simulation of materials with strong electron correlations. With the advent of quantum gas microscopy, we now have the abilities to observe and manipulate these systems at the level of single atoms and lattice sites. In this talk, I will describe how we perform microscopy on fermionic 40K, and how we realize the two-dimensional Fermi-Hubbard model, a paradigm believed to capture the essence of high-Tc superconductivity in the cuprates. I will then discuss two experiments we performed using this system. In the first, we examined spatial spin and charge correlations in a fermionic Mott insulator. At half-filling, we observed antiferromagnetic spin correlations in the presence of doublon-hole bunching. Upon doping, these spin correlations weakened monotonically, and an interaction-enhanced Pauli hole emerged, a real-space manifestation of Pauli-blocking. In the second, we measured the spin conductivity of a homogeneous Mott insulator at half-filling, a quantity which is difficult to measure in the cuprates, and highly challenging to calculate theoretically. For strong interactions, we observed diffusive spin transport driven by super-exchange and doublon-hole assisted tunneling. Extending the technique developed for this measurement to finite doping could shed light on the complex interplay between spin and charge in the Hubbard model.